In a joint statement issued after talks with Iran in Beijing, Beijing and Moscow also said they welcomed Iran's reiteration that its nuclear program was exclusively for peaceful purposes, and that Iran's right to peaceful uses of nuclear energy should be "fully" respected.
In 2015, Iran agreed to curb its nuclear program in exchange for the lifting of international sanctions in a deal with the US, Russia, China, Britain, France and Germany.
But in 2018, Donald Trump, a year into his first term as US president, pulled out of the pact.
"(China, Russia and Iran) emphasised that the relevant parties should be committed to addressing the root cause of the current situation and abandoning sanction, pressure or threat of force," China's Vice-Foreign Minister Ma Zhaoxu told reporters after the meeting on Friday.
China, Russia and Iran also emphasised the necessity of terminating all "unlawful" unilateral sanctions, Ma said.
Ma's meeting with Russian Deputy Foreign Minister Sergei Ryabkov and Iranian Deputy Foreign Minister Kazem Gharibabadi came days after Tehran spurned US "orders" to resume dialogue over the nuclear program.
Last week, Trump said he had sent a letter to Iran's Supreme leader Ayatollah Ali Khamenei proposing nuclear talks, adding that "there are two ways Iran can be handled: militarily or you make a deal".
Iranian President Masoud Pezeshkian responded that he would not negotiate with the US while being "threatened", and Iran would not bow to US "orders" to talk.
Iran was further enraged after six of the United Nations Security Council's 15 members - the US, France, Greece, Panama, South Korea and Britain - held a closed-door meeting this week to discuss its nuclear program.
Tehran said the meeting was a "misuse" of the UN Security Council.
Iran has long denied that it is working on developing a nuclear weapon.
But the International Atomic Energy Agency warned in February that Tehran was "dramatically" accelerating enrichment of uranium to near the roughly 90 per cent weapons-grade level.
